Xin Q. Diesel Engine System Design

348

5

Engine–vehicle matching analysis in diesel

powertrain system design

Abstract: This chapter discusses vehicle powertrain performance and the

impact on diesel engine system design in ring operation. It begins by

summarizing the formulae of vehicle performance analysis, followed by

analytical engine–vehicle matching methods with engine characteristic

maps for optimum fuel economy and drivability. It then describes the

transient powertrain performance simulations of vehicle driving cycles and

acceleration. It emphasizes the concept of ‘top–down’ powertrain design

approach to optimize the interface between the vehicle and the engine.

Hybrid powertrain performance analysis is also briey introduced.

Key words: vehicle performance, drivetrain, powertrain dynamics,

engine–vehicle matching, driving cycle, fuel economy, drivability, transient

performance, hybrid.

5.1 The theory of vehicle performance analysis

5.1.1 Introduction of vehicle analysis areas

Automotive engines are designed for real-world vehicle operating needs.

Engine development is focused on improving engine cycle processes and

torque curve shape. At the same time, it strives to reduce parasitic losses

and fuel consumption. Drivetrain design is focused on increasing drivetrain

efciency, reducing resistance forces, and selecting proper transmission

ratios to match the engine. Engine–vehicle system integration for the diesel

powertrain requires a close collaboration between the two. Among the

four major areas of vehicle dynamics (powertrain transmission, braking,

suspension, and steering systems), the rst two areas are directly related to

engine system design.

The following topics are important in vehicle performance analysis for

engine system design: longitudinal dynamics and vehicle force distribution,

tire–road rolling resistance, aerodynamic drag resistance, vehicle inertia force,

transmission and torque converter modeling, vehicle acceleration calculation,

and vehicle fuel economy calculation.

Heavy-duty vehicle drivetrain design fundamentals are introduced in

Jones (1991). Powertrain design process is discussed by Dopson et al. (1995)

and Ferraz et al. (2001). Vehicle powertrain simulation methodologies are

presented by Morel et al. (1999), Ciesla et al. (2000), and Guzzella and

Diesel-Xin-05.indd 348 5/5/11 11:49:13 AM

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349Engine–vehicle matching in diesel powertrain system design

Sciarretta (2005). Heavy-duty vehicle test cycles are investigated by Bata

et al. (1994) and Clark et al. (2003). The coastdown method is discussed

by Petrushov (1997) and Miller (2004). Overviews on vehicle fuel economy

are provided by Ehlbeck and Mayenburg (1991), Simner (1996), Patton et

al. (2002) and Sovran and Blaser (2003). Transmission efciency has been

researched by Kluger and Greenbaum (1993). Torque converter design and

performance are reviewed by Mercure (1979). The SAE procedures listed

in the section of references at the end of this chapter also provide valuable

fundamental information on vehicle, powertrain and drivetrain.

5.1.2 Formulae of vehicle performance analysis

Heavy-duty trucks are usually front-engined and rear-wheel-driven in order to

obtain effective engine cooling and better tractive force during acceleration and

upgrade climbing. In order for a vehicle to move, the tractive force provided

by the engine and the transmission needs to be greater than the total of all

static resistance forces. However, the maximum tractive force acting on the

vehicle driving wheels is limited by the tire–road adhesion force, even if the

engine and the transmission can produce a higher tractive force.

The vehicle force balance at any steady-state or transient condition can

be written as

F

t

+ F

er

+ F

acc

+ F

br

+ F

rf

+ F

a

+ F

i

+ F

gl

+ F

dr

= 0 5.1

When the vehicle moves at a constant speed, the inertia force F

i

= 0. If F

i

is

not equal to zero, the vehicle either accelerates or decelerates in transients.

F

t

is the tractive force acting on the vehicle wheels and is delivered from

engine ring operation. Note that the tractive force due to engine ring is

dened as a positive value, and all resistance forces are dened as negative

values. During engine ring, the engine brake retarding force F

er

= 0. F

acc

is a vehicle equivalent resistance force acting on the wheels and caused

by accessory loads such as the cooling fan, the air conditioning and the

power steering. If the driver does not use the service brake (wheel brake),

the service brake force F

br

= 0. F

rf

is the tire–road rolling friction force. F

a

is the aerodynamic resistance force. F

gl

is the gravity force on a gradient.

F

dr

is the resistance force of drivetrain retarders such as the hydrodynamic

or electromagnetic retarder. During engine ring without wheel braking or

drivetrain retarder braking, the tractive force acting on the vehicle wheels

is given by

F

t

= – (F

acc

+ F

rf

+ F

a

+ F

i

+ F

gl

). 5.2

On the other hand, the maximum allowable tractive force is limited by the

tire–road adhesion force, which is equal to the normal load multiplied by

the road adhesion coefcient. The adhesion force is determined by the axle

Diesel-Xin-05.indd 349 5/5/11 11:49:13 AM

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350 Diesel engine system design

load, the road surface condition and the tires. For example, an icy road has

a very low adhesion force, and the vehicle wheels may slip on the ice. It

should be noted that each term in the vehicle force balance equation 5.1 is

for the total vehicle mass m

v

(including trailers, if any).

The gravity force is given by F

gl

= m

v

g sin q, and the road grade is de ned

as G

r

= tan q, where q is the road slope angle (positive for downhill, negative

for uphill), and g is the acceleration due to gravity. The rolling friction

resistance is calculated by F

rf

= – m

v

g · f

rf

cos q if the aerodynamic lift force

is ignored in the net normal load. The tire rolling friction coef cient f

rf

increases when the vehicle speed, the tractive force, or the tire tilting angle

increases. The friction coef cient decreases when the tire pressure or the tire

temperature increases. The tire rolling friction coef cient is also affected by

tire structure, tire material and road surface condition. The friction coef cient

is independent of the vertical load. Usually, the rolling friction coef cient

values are between 0.005 and 0.01 on a concrete road surface. Moreover,

for a radial-ply truck tire, when N

v

< 100 km/hour, previous experimental

data gave f

rf

= 0.006 + 0.23(0.001N

v

)

2

, where N

v

is vehicle speed; and for

a bias-ply truck tire, f

rf

= 0.007 + 0.45(0.001N

v

)

2

(Wong, 1993).

The aerodynamic resistance force is calculated by

Ff

AN

Ff

aA

Ff

MB

Ff

av

Ff

av

Ff

AN

av

AN

vw

Ff= – Ff

Ff

aA

Ff= – Ff

aA

Ff

,

05

Ff05Ff

Ff

aA

Ff05Ff

aA

Ff

2

Ff

aA

Ff.Ff

aA

Ff

aA

Ff05Ff

aA

Ff.Ff

aA

Ff05Ff

aA

Ff

r

Ff

r

Ff

aA

Ff

r

Ff

aA

Ff

where r

AMB

is the ambient air density, f

a

is the aerodynamic resistance

coef cient, A

v

is the projected frontal area of the vehicle in the direction of

travel, and N

vw

is the vehicle speed relative to the wind.

The transient inertia force is given by F

i

= – xm

v

a

v

, where m

v

is the total

effective vehicle mass including the payload, and a

v

is the vehicle’s linear

acceleration. The x is the rotational mass coef cient which is de ned as the

ratio of the total vehicle inertia force to the linear inertia force. The total

refers to the sum of the inertia force caused by both the linear motion of

the vehicle mass and the equivalent inertia force caused by all the rotating

masses. The x can be derived as follows:

x

h

= 1 +

x

= 1 +

x

+

2

I

mr

IC

ii

mr

dr

iv

e

v

mr

v

mr

tir

mr

tir

mr

e

Et

IC

Et

IC

rg

ii

rg

ii

EtrgEt

ra

ii

ra

ii

xt

h

xt

h

raxtra

v

mr

v

mr

tir

mr

tir

mr

e

22

ii

22

ii

22

2222

+

22

+

22

d

IC

ii

N

mr

22

mr

22

a

i

t

Et

IC

Et

IC

rg

ii

rg

ii

EtrgEt

ra

ii

ra

ii

xt

raxtra

v

mr

v

mr

tir

mr

tir

mr

ev

a

ev

a

gr

2

h

xt

h

xt

Ê

Ë

Á

Ê

Á

Ê

Ë

Á

Ë

ˆ

¯

˜

ˆ

˜

ˆ

¯

˜

¯

5.3

where r

tire

is the dynamic tire radius, I

drive

is the total equivalent mass

moment of inertia of all the driveline components including vehicle wheels,

I

E

is the moment of inertia of the engine rotating components connected to

the driveline such as the  ywheel, i

gr

is the transmission gear ratio, i

ax

is

the overall drive axle gear ratio, t is time, and h

t

is the drivetrain ef ciency

representing the frictional power losses of the entire drivetrain (from the

engine crankshaft to the vehicle wheels, including the clutch or the torque

converter, the transmission, the universal joints, the differential, the drive

axles, the  nal drive gear, etc.). Note that vehicle accessory power is de ned

as a resistance power rather than a frictional power loss.

Diesel-Xin-05.indd 350 5/5/11 11:49:14 AM

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351Engine–vehicle matching in diesel powertrain system design

The drivetrain ef ciency of manual transmissions can be around 95%

at lower gears and 97–98% at the 1:1 direct transmission top gear. The

ef ciency of automatic transmissions is roughly 10% lower. The overall

drivetrain ef ciency of heavy-duty trucks and buses usually peaks around

80–90%. The ef ciency varies widely at different engine speeds, loads and

gear numbers (Kluger and Greenbaum, 1993). C

tr

in equation 5.3 is the

torque ratio of the torque converter used with an automatic transmission

(for manual transmissions without the torque converter, C

tr

can be set to

1). Torque converter ef ciency is h

Tv

= C

sr

C

tr

, where the speed ratio C

sr

is

de ned as the output speed divided by the input speed, and the torque ratio

C

tr

is de ned as the output torque divided by the input torque. When locked

up without hydraulic coupling, the torque converter ef ciency reaches its

highest value. C

sr

and C

tr

are obtained from the characteristic chart of the

torque converter when the input capacity factor c

Tv

is known. Note that

c

Tv

= N

Tv

/J

Tv

0.5

, where N

Tv

is speed and J

Tv

is torque. The torque converter

input capacity factor c

Tv

is equal to the engine capacity factor c

E

, which is

calculated using c

E

= N

E

/J

E

0.5

, where N

E

is the engine speed and J

E

is the

engine torque. In the last term of equation 5.3, the transient gear ratio change

di

gr

/dt can produce a signi cant resistance inertia force for continuously

variable transmissions. The x can be approximated by an empirical formula

x

= 1 + 0.04 + 0.0025

x

= 1 + 0.04 + 0.0025

x

ii

gr

ii

gr

ii

ax

22

ii

22

ii

(Wong, 1993). The x in equation 5.3 is a very

important parameter that includes the engine moment of inertia. Based on

equation 5.3 the transient powertrain equation 5.20 is derived later.

The vehicle tractive force acting on the wheels F

t

, the tractive torque J

t

,

and the engine brake torque J

E

are related by the following relationship:

F

J

r

JC

ii

r

t

F

t

F

t

tir

r

tir

r

e

Et

JC

Et

JC

rg

ii

rg

ii

EtrgEt

ra

ii

ra

ii

xt

raxtra

tir

r

tir

r

e

=

h

xt

h

xt

5.4

The engine  ring brake torque at the crankshaft can be calculated by

J

FF

Fr

Ci

i

E

ac

FF

ac

FF

cr

FF

cr

FF

fa

FF

fa

FF

crfacr

ig

FF

ig

FF

Fr

ig

Fr

l

Fr

l

Fr

tir

Fr

tir

Fr

e

tr

Ci

tr

Ci

gr

=

– (

FF +FF

FF

cr

FF +FF

cr

FF

cr

FF

cr

FF FF

cr

FF

fa

crfacr

+

fa

+

fa

FF +FF

FF FF

ig

FF

ig

FF FF

ig

FF

+

ig

+

ig

)

Fr)Fr

ax

aaxa

t

h

ax

h

ax

5.5

The engine speed can be calculated by

N

Ni

i

rC

f

E

vg

Ni

vg

Ni

ra

i

ra

i

x

raxra

tir

rC

tir

rC

es

rC

es

rC

rs

f

rs

f

lip

=

(

rs

(

rs

–

rs

–

rs

)

21

rs

21

rs

21

rC21rC

rC

tir

rC21rC

tir

rC

es

21

es

rC

es

rC21rC

es

rC

rs

21

rs

(21(

rs

(

rs

21

rs

(

rs

p

21

p

21

5.6

where N

E

is the engine speed (revolution per second), f

slip

is the slip of

the vehicle running gear, f

slip

= 2–5% (Wong, 1993), C

sr

is the speed ratio

of the torque converter used with an automatic transmission (for manual

transmissions without torque converter, C

sr

can be set to 1). Engine brake

power can be calculated by



WJ

N

EE

WJ

EE

WJ

E

WJ =WJ

WJ

EE

WJ =WJ

EE

WJ

5.7

Diesel-Xin-05.indd 351 5/5/11 11:49:15 AM

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352 Diesel engine system design

Note that the term ‘brake power’ derives from the engine dynamometer that

absorbs power by the action of a brake (e.g., a friction brake). The engine

‘brake power’ refers to the crankshaft net power which is input to the vehicle

drivetrain in either  ring or braking operation, and it is not the same as the

engine ‘braking power or retarding power’ in engine brake operation. Figure

5.1 illustrates the vehicle tractive force characteristics with a seven-speed

transmission.

Denoting t as time, vehicle acceleration a

v

is calculated by:

a

N

t

m

FF

F

v

ac

FF

ac

FF

ct

FF

ct

FF

rf

FF

rf

FF

ag

FF

ag

FF

F

ag

F

l

=

d

NdN

d

=

(

FF +FF

FF

ct

FF +FF

ct

FF

ct

FF

ct

FF FF

ct

FF

+

FF +FF

FF FF

ag

FF

ag

FF FF

ag

FF

+

ag

+

ag

)

1

(

1

(

x

m

x

m

(

x

(

5.8

Vehicle speed is calculated by

NN

at

vt

NN

vt

NN

vt

v

at

v

at

t

,,

vt,,vt

21

NN

21

NN

vt

21

vt

,,

21

,,

vt,,vt

21

vt,,vt

1

2

NN =NN

NN

21

NN =NN

21

NN

21

NN

21

NN NN

21

NN

vt

21

vt

21

vt

+

d

atdat

Ú

t

Ú

t

5.9

Vehicle travel distance is given by

ll

Nt

vt

ll

vt

ll

vt

v

Nt

v

Nt

t

,,

vt,,vt

21

ll

21

ll

vt

21

vt

,,

21

,,

vt,,vt

21

vt,,vt

1

2

ll =ll

ll

21

ll =ll

21

ll

21

ll

21

ll ll

21

ll

vt

21

vt

21

vt

+

d

NtdNt

Ú

t

Ú

t

5.10

Vehicle acceleration time is calculated by

D

Ê

Ë

Ê

Á

Ê

Ë

Á

Ë

ˆ

¯

ˆ

˜

ˆ

¯

˜

¯

◊

ÚÚ

tt

ÚÚ

tt

ÚÚ

a

N

m

F

ac

tt

ac

tt

t

ÚÚ

t

ÚÚ

t

ÚÚ

t

ÚÚ

v

N

ÚÚ

N

ÚÚ

N

v

ac

F

ac

F

c

v

tt =tt

d

ÚÚ

d

ÚÚ

tt dtt

ÚÚ

tt

ÚÚ

d

ÚÚ

tt

ÚÚ

=

ÚÚ

d

Ê

d

Ê

Ë

d

Ë

Ê

Ë

Ê

d

Ê

Ë

Ê

Á

Ê

d

Ê

Á

Ê

Ë

Á

Ë

d

Ë

Á

Ë

Ê

Ë

Ê

Á

Ê

Ë

Ê

d

Ê

Ë

Ê

Á

Ê

Ë

Ê

ˆ

d

ˆ

¯

d

¯

ˆ

¯

ˆ

d

ˆ

¯

ˆ

˜

ˆ

d

ˆ

˜

ˆ

¯

˜

¯

d

¯

˜

¯

ˆ

¯

ˆ

˜

ˆ

¯

ˆ

d

ˆ

¯

ˆ

˜

ˆ

¯

ˆ

ÚÚ

d

ÚÚ

N dN

=

1

ÚÚ

1

ÚÚ

2

ÚÚ

1

2

1

d

1

d

x

+

++ +

+

d

FF

+FF +

FF

+FF +

N

dNd

tr

FF

tr

FF

+FF +

tr

+FF +

fa

+

fa

+

FF

fa

FF

trfatr

tr

fa

tr

gl

FF

gl

FF

N

v

Ê

Ë

Á

Ê

Á

Ê

Ë

Á

Ë

ˆ

¯

˜

ˆ

˜

ˆ

¯

˜

¯

Ú

N

Ú

N

1

2

5.11

where F

t

is the transient vehicle tractive force resulting from the available

engine transient torque during acceleration in each gear. It should be noted

that under the same fueling rate the transient engine torque is usually lower

than the steady-state engine torque due to losses in combustion, pumping loss,

turbocharger lag, and thermal inertia. In some cases the transient power can

be 5–8% lower than the steady-state power. It is observed that the vehicle

acceleration time from the speed N

v1

to N

v2

is the area under the curve of

‘the reciprocal of acceleration vs. vehicle speed’, plus the gear-shifting

time (typically 0.2–0.6 s for each gear change). The area under the curve

depends on where the transmission gear is shifted. Figure 5.2 shows the

vehicle acceleration characteristics with the full load engine torque curve

for a seven-speed transmission calculated using equation 5.8.

Vehicle dynamics can also be expressed by a power balance as

follows:

Diesel-Xin-05.indd 352 5/5/11 11:49:16 AM



Adhesion limit of dry

concrete road

Adhesion limit

of icy road

Road grade,

aerodynamic and

rolling friction

resistance forces

Vehicle tractive force

Uphill

Level

Downhill

Piston engines cannot produce very high power at low engine speed because its

peak torque is limited. A transmission is needed in order to increase tractive force

Vehicle speed

Over-design

Force reserved for uphill

climbing or acceleration

Design control point at maximum

vehicle speed (near rated power)

This is the constant power curve.

Vehicle power = tractive force times vehicle speed

This is the direction of good drivability. A

smooth constant power curve is ideal for

drivetrain matching. The gaps underneath

power curve are due to discrete gear

numbers and the gaps impede drivability

If the lug curve is shifted up to the dotted

curve, it is an over-design because the vehicle

power at maximum vehicle speed should not

include hill climbing and acceleration

Engine lug curve

at ﬁrst gear and

second gear

Design control

point at maximum

torque

5.1 Vehicle tractive force characteristics.

Diesel-Xin-05.indd 353 5/5/11 11:49:16 AM

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354 Diesel engine system design



WW

ta

WW

ta

WW

cc

WW

rf

WW

rf

WW

rf

WW

ai

WW

ai

WW

ai

WW

g

WW

g

WW

= – (

WW = – (WW

ta

= – (

ta

WW

ta

WW = – (WW

ta

WW

+

WW WW

WW

rf

WW WW

rf

WW

WW+ WW

+

ai

+

ai

WW WW

ai

WW

ai

WW WW

ai

WW

WW+ WW

)

5.12

where



WW

ac

WW

ac

WW

cE

WW

cE

WW

ac

ct

WW =WW

WW

cE

WW =WW

cE

WW

(

WW (WW

cE

(

cE

WW

cE

WW (WW

cE

WW

ac

(

ac

ct

(

ct

–

ct

–

ct

)

,

(

,

(

2

ct

2

ct

h

ct

h

ct

5.13



WW

FN

tE

WW

tE

WW

tt

FN

tt

FN

v

WW =WW

WW

tE

WW =WW

tE

WW

tt

tE

WW

tE

WW WW

tE

WW

=

tt

=

tt

h

tE

h

tE

h

5.14

The engine brake power can be calculated by



W

FF

FN

E

W

E

W

ac

FF

ac

FF

cr

FF

cr

FF

fa

FF

fa

FF

crfacr

ig

FF

ig

FF

FN

ig

FN

lv

FN

lv

FN

t

=

– (

FF +FF

FF

cr

FF +FF

cr

FF

cr

FF

cr

FF FF

cr

FF

fa

crfacr

+

fa

+

fa

FF +FF

FF FF

ig

FF

ig

FF FF

ig

FF

+

ig

+

ig

)

FN)FN

lv

)

lv

FN

lv

FN)FN

lv

FN

h

5.15

Figure 5.3 illustrates the vehicle tractive power characteristics with a

six-speed transmission. Unlike the torque calculation, the calculation of

the required engine power in equation 5.15 does not relate to the drivetrain

transmission ratio. The difference between the engine brake power and the

vehicle accessory power is the net available power at the inlet of the clutch

or the torque converter to drive the vehicle. Figure 5.4 shows the calculated

vehicle power requirements under different running conditions.

0 10 20 30 40 50 60 70 80 90 100 110

1 mph = 1.609 km/hr

Vehicle speed (mph)

Reciprocal of vehicle acceleration (1/aV)

6

5

4

3

2

1

0

The area enveloped under gear

7 is the acceleration time from

40 to 50 mph with gear 7

Gear 7

Gear 3

Gear 6

Gear 5

Gear 4

Ideal curve for minimum

acceleration time

Gear 2

Gear 1

5.2 Vehicle acceleration characteristics.

Diesel-Xin-05.indd 354 5/5/11 11:49:17 AM

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355Engine–vehicle matching in diesel powertrain system design

5.2 Engine–vehicle steady-state matching in engine

ﬁring operation

5.2.1 Overview of matching criteria

Drivability refers primarily to a wide range of physical experience felt while

driving including acceleration, deceleration, gradeability, transition between

engine operating modes and gear shifts, as well as powertrain NVH during

the events of tip-in, tip-out, takeoff, gearshift, etc. Drivability evaluation is

related to the entire vehicle dynamics engineering and controls, including the

engine, the engine mount stiffness and damping, the powertrain command

and the management of torque-demand coordination, the gearbox stiffness

and inertia, the clutch, the drivetrain, the wheels, the tires, the suspension,

the vehicle body, etc. However, in engine system design, the vehicle driving

performance is usually determined by three aspects: (1) the maximum vehicle

speed on level ground; (2) acceleration time; and (3) the maximum gradeability

under a combined vehicle weight rating at constant speed in rst gear. Overall

vehicle transient acceleration performance is usually characterized by the

time taken to accelerate from 0 to 60 mph, shifting from rst gear to near

the highest gear. Alternatively, it can be characterized by the time spent to

cover a distance of 400 meters. Vehicle launch capability is measured by

the time to accelerate from 5 to 35 mph. Vehicle overtaking capability is

measured by the time to accelerate from 35 to 60 mph or 60 to 80 mph during

Vehicle weight 16 000 lbs, rear axle ratio 3.70

Vehicle power (hp)

250

200

150

100

50

0

0 10 20 30 40 50 60 70 80 90 100 110

Vehicle speed (mph)

The gap here

indicates the

power reserve

for acceleration

or gravity uphill

Total vehicle

resistance

power (rolling

friction plus

aerodynamic)

Total resistance

power (add 6%

uphill gravity)

Engine lug curve

at gear 1

Engine lug curve

at gear 2

Engine lug curve

at gear 3

Engine lug curve

at gear 4

Engine lug curve

at gear 5

Engine lug curve

at gear 6

5.3 Vehicle tractive power characteristics.

Diesel-Xin-05.indd 355 5/5/11 11:49:17 AM

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356 Diesel engine system design

acceleration in a high gear. The maximum desirable gradeability is usually

less than 8% uphill grade on highway for heavy-duty commercial vehicles,

and approximately 12–16% in mountains. The maximum gradeability is also

related to the vehicle’s startability.

Vehicle fuel economy is measured by miles per gallon of fuel (mpg) or

liters of fuel per 100 km of travel. Several methods exist to evaluate fuel

economy.

Sensitivity analysis on the effects of vehicle weight and

speed on the power at wheel due to grade gravity resistance

at 7% uphill grade

Vehicle weight (lbs)

5000 10000 15000 20000 25000

Engine brake power required = (wheel

power)/(total drivetrain efﬁciency)

This condition requires

231 hp engine brake power

with 87% drivetrain efﬁciency

to only overcome 7% uphill

gravity force resistance, or

requires 402 hp with 50%

drivetrain efﬁciency

30 mph

40 mph

50 mph

60 mph

70 mph

Power at wheel due to uphill

grade gravity resistance (hp)

0

–50

–100

–150

–200

–250

–300

Sensitivity analysis on the effects of vehicle weight and

acceleration on the power at wheel due to acceleration

resistance on level road at 40 mph

Vehicle weight (lbs)

0 5000 10000 15000 20000 25000

Engine brake power required = (wheel

power)/(total drivetrain efﬁciency)

This condition requires 268

hp engine brake power with

87% drivetrain efﬁciency to

overcome acceleration

resistance, or requires 466 hp

with 50% drivetrain efﬁciency

1.0 mph/s

1.5 mph/s

2.0 mph/s

2.5 mph/s

3.0 mph/s

Power at wheel due to inertia

acceleration resistance (hp)

0

–50

–100

–150

–200

–250

–300

–350

–400

–450

–500

1 mph = 1.609 km/hr

1 hp = 0.7457 kW

1 lbm = 0.4536 kg

5.4 Vehicle power requirements under different operating conditions.

Diesel-Xin-05.indd 356 5/5/11 11:49:18 AM

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357Engine–vehicle matching in diesel powertrain system design

1. A curve of the fuel amount consumed in liters per 100 km during cruising

at each constant vehicle speed plotted versus the vehicle speed.

2. The fuel amount consumed in mpg or liters per 100 km for a speci c

driving cycle.

3. The weighted average fuel consumption, for example, the US EPA’s

CAFE composite fuel economy indicator, de ned as

h

hh

FC

composite

hh

FC

hh

ur

hh

ban

hh

FC

hi

,,

composite,,composite

mp

g

,,

hh

,,

hh

ur

hh

,,

hh

ur

hh

ban

hh

,,

hh

ban

hh

FC,,FC

=

1

0.55

+

04

5

.

04.04

ghway

gghwayg

5.16

where h

FC,urban

is the fuel economy of the city (urban) driving cycle

in mpg, and h

FC,highway

is the fuel economy of the highway (suburban)

driving cycle in mpg.

4. Fuel economy during full-pedal acceleration.

The total fuel mass consumed during a driving cycle can be calculated

by

mm

tW

t

fuel

mm

fuel

mm

t

BSFC

tW

BSFC

tW

E

tW

E

tW

t

mm =mm

d

mm dmm

(

tW (tW

)d



1

2

ÚÚ

mm

ÚÚ

mm

tW

ÚÚ

tW

fuel

ÚÚ

fuel

t

ÚÚ

t

ÚÚ

t

ÚÚ

t

d

ÚÚ

d

mm dmm

ÚÚ

mm dmm

fuel

d

fuel

ÚÚ

fuel

d

fuel

tW =tW

ÚÚ

tW =tW

(

ÚÚ

(

tW (tW

ÚÚ

tW (tW

d



d

ÚÚ

d



d

1

ÚÚ

1

2

ÚÚ

2

h

tW

h

tW

(

h

(

5.17

where



m

fuel

is the fuel  ow rate and h

BSFC

is the engine BSFC. If treated

as a quasi steady-state approximation, the BSFC at any non-idle condition

(i.e., engine brake power greater than zero) can be determined at each engine

speed–load point of the driving cycle from the engine BSFC map. The real

transient BSFC must be computed by a high- delity crank-angle-resolution

engine cycle simulation model that re ects the transient combustion ef ciency

and heat losses, as well as the transient pumping loss during turbo lag which

is related to engine controls. A similar approach can be used to compute

the total emissions over the driving cycle if the engine emissions maps

are available. Engine brake power can be computed by vehicle powertrain

transient simulation considering the acceleration inertia effect (equation

5.3). It should be noted that during vehicle deceleration, the fuel rate



m

fuel

is either the idle fueling amount or zero (especially during engine braking),

depending on the vehicle fueling calibration strategy and the use of engine

brake. If the vehicle cruises at a constant speed N

v

to travel a distance L

v

,

the fuel mass consumed can be calculated in simpli ed form as:

mW

l

N

fuel

mW

fuel

mW

BSFC

mW

BSFC

mW

E

mW

E

mW

v

mW =mW

h

mW

h

mW



Ê

Ë

Ê

Ë

Ê

Á

Ê

Ë

Á

Ë

Ê

Ë

Ê

Á

Ê

Ë

Ê

ˆ

¯

ˆ

¯

ˆ

˜

ˆ

¯

˜

¯

ˆ

¯

ˆ

˜

ˆ

¯

ˆ

5.18

Engine–vehicle matching analysis was discussed by Chana et al. (1977),

Wong and Clemens (1979), Thring (1981), Phillips et al. (1990), Fluga (1993),

Watson (1995), Jawad et al. (1999), Mikulec and Li (2000), Walker and Ford

Diesel-Xin-05.indd 357 5/5/11 11:49:19 AM

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Xin Q. Diesel Engine System Design

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